Target Corp.'s computer security staff raised concerns about vulnerabilities in the retailer's payment card system at least two months before hackers stole 40 million credit and debit card numbers from its servers, people familiar with the matter said.

At least one analyst at the Minneapolis-based retailer wanted to do a more thorough security review of its payment system, a request that at least initially was brushed off, the people said. The move followed memos distributed last spring and summer by the federal...